derivative f(x)=2x^3+3x^2-12x+2

解

導関数

f (x) = 2 x^{3} + 3 x^{2} - 12 x + 2

6 x^{2} + 6 x - 12

解答ステップ

\frac{d}{d x} (2 x^{3} + 3 x^{2} - 12 x + 2)

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (2 x^{3}) + \frac{d}{d x} (3 x^{2}) - \frac{d}{d x} (12 x) + \frac{d}{d x} (2)

\frac{d}{d x} (2 x^{3}) = 6 x^{2}

\frac{d}{d x} (3 x^{2}) = 6 x

\frac{d}{d x} (12 x) = 12

\frac{d}{d x} (2) = 0

= 6 x^{2} + 6 x - 12 + 0

簡素化

= 6 x^{2} + 6 x - 12